${5 \div \dfrac{4}{9} =}$
${5} \div \dfrac{4}{9}} ={\dfrac{5}{1}} \div \dfrac{4}{9}} $ $~~~~~~~{\gray{\text{Rewrite 5 as }\dfrac{5}{1}}}. $ $\phantom{5 \div \dfrac{2}{3}}} ={\dfrac{5}{1}} \times \dfrac{9}{4}}$ $ ~~~~~~{\gray{\text{Multiply by reciprocal of }\dfrac{4}{9}.}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{{5}\times9}}{1\timesD4}} $ $~~~~~~~{\gray{\text{Multiply. }}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{45}{4}} $ ${5 \div \dfrac{4}{9} =\dfrac{45}{4}}$ [Wait, can we rewrite the answer as a mixed number?]